A1 Refereed original research article in a scientific journal
Minimal normal measurement models of quantum instruments
Authors: Pellonpää Juha-Pekka, Tukiainen Mikko
Publisher: PERGAMON-ELSEVIER SCIENCE LTD
Publication year: 2017
Journal: Reports on Mathematical Physics
Journal name in source: REPORTS ON MATHEMATICAL PHYSICS
Journal acronym: REP MATH PHYS
Volume: 79
Issue: 3
First page : 261
Last page: 278
Number of pages: 18
ISSN: 0034-4877
eISSN: 1879-0674
DOI: https://doi.org/10.1016/S0034-4877(17)30040-X
Self-archived copy’s web address: https://arxiv.org/abs/1509.08886
Abstract
In this work we study the minimal normal measurement models of quantum instruments. We show that usually the apparatus' Hilbert space in such a model is unitarily isomorphic to the minimal Stinespring dilation space of the instrument. However, if the Hilbert space of the system is infinite-dimensional and the multiplicities of the outcomes of the associated observable (POVM) are all infinite then this may not be the case. In these pathological cases the minimal apparatus' Hilbert space is shown to be unitarily isomorphic to the instrument's minimal dilation space augmented by one extra dimension.
In this work we study the minimal normal measurement models of quantum instruments. We show that usually the apparatus' Hilbert space in such a model is unitarily isomorphic to the minimal Stinespring dilation space of the instrument. However, if the Hilbert space of the system is infinite-dimensional and the multiplicities of the outcomes of the associated observable (POVM) are all infinite then this may not be the case. In these pathological cases the minimal apparatus' Hilbert space is shown to be unitarily isomorphic to the instrument's minimal dilation space augmented by one extra dimension.
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